The appeal process by Zaw Lin and Wai Phyo, both 22, is expected to drag on for years, extending the anguish for the families of the two victims.

It will also again place attention on the contentious roles played in an overseas death penalty case by British detectives dispatched by David Cameron to observe the work of their Thai counterparts.

“Zaw Lin and Wai Phyo both repeated their sorrow and sympathy for Hannah and David’s families, but they insist they had nothing to do with their deaths,” Andy Hall, a Bangkok-based British migrant rights activist, told the Telegraph after visiting the men on death row last week.

Hannah Witheridge and David MillerCredit:
PA

“They remain hopeful that that justice will be done and their names will be cleared.”

Ms Witheridge was raped and she and Mr Miller were savagely bludgeoned to death with a wooden hoe as they walked back to their hotel rooms late at night along a beach in Sept 2014.

The investigation was dogged by mis-steps amid deepening questions about Thailand’s reputation as a safe tourist idyll.

With the Thai junta making the case a priority, the two Burmese bar workers were arrested in early October.

The pair initially confessed to the killings but quickly retracted their statements, saying they were tortured.

The three judges who handed down the guilty verdicts and death penalties concluded that the prosecution proved its case with forensic evidence that met “international standards” linking the two men to the murders.

The appeal submitted on Monday morning was put together over five months by the defence legal team from the Lawyers Council of Thailand, supported by Burmese, Australian and British translators, assistants and advisors.

One of those defence advisors, Jane Taupin, a renowned Australian forensic scientist, told the Telegraph that documents explaining how Thai investigators matched the two men’s DNA to the victims were not submitted and other paperwork had hand-written changes.

The mother of Wai Phyo breaks into tears after the court issued a death sentenceCredit:
RUNGROJ YONGRIT/EPA

Ms Taupin noted that the highly complex standards for DNA matching based on statistical probability were not provided. And she also pointed out that there were serious questions about the chain of custody of the DNA samples.

There have also been persistent questions about the accreditation of the laboratory that handled the forensic evidence.

"The scientific records were lacking and so it is impossible to determine whether they meet international standards,” Ms Taupin said. “I certainly do not see that the court could conclude that the forensic evidence met those international standards.”

Pornthip Rojanasunand, Thailand’s best-known forensic scientist, testified for the defence that the crime scene was not protected and the collection of evidence "contradicted the principles of forensic science".

The prosecution said that DNA taken from the accused men matched samples recovered from the body of Miss Witheridge.

The convictions apparently split the families of the victims. Mr Miller’s parents and brother issued a powerful statement saying that justice had been done with the Christmas Day verdicts after sitting through much of the trial.

Ms Witheridge’s family have not made a formal comment. But her sister Laura later issued a blistering attack on the Thai police for its “bungled” investigation into the killings.

She claimed that she had received death threats, said that her family was offered money to keep quiet after the murders and accused the Thai authorities of “covering-up” the killings of other Western tourists on Koh Tao.